“…This has been done in several different ways: just to quote a few, the Brakke varifold-solution [15], the viscosity solution (see [30] and references therein), the Ilmanen elliptic regularization [37], the level-set theoretic subsolution and the minimal barrier solution (see [12] and references therein), the Almgren-Taylor-Wang [1] and Luckhaus-Sturzenhecker [42] solutions, next included by De Giorgi into his notion of minimizing movement and generalized minimizing movement (GMM) [21,22]; see also [16,24,47]. Some of those solutions (e.g., the Brakke solution [15,54], the GMM solution [14], the elliptic regularization [50]) can be adapted to treat the multiphase case at least in the Euclidean case, especially those that do not rely heavily on the comparison principle. Also, the existence of a distributional solution of mean curvature evolution of partitions on the torus using the time thresholding method introduced in [46] has been proved in [41]; see also [39].…”